Showing object axis in Blender 2.8
You can do one of two things:


You can select the 'Move' tool in the toolbar (T) or press Shift+Space> G:





If you would like the gizmo to appear regardless of the tool you have selected, click the 'Viewport Gizmos' button in the 3D View header, enable gizmos for active object by enabling the 'Active Object' option and then enable the 'Move', 'Rotate' or 'Scale' options:




Note: Both these options require the object to be selected for the gizmo to appear. If no gizmos are appearing, make sure gizmos are enabled by clicking the 'Show Gizmos' button: